A machine tool of the species described hereinabove is known (brochure "Dyna-M" of the machine tool laboratory of RWTH Aachen, September 1997). In the construction style known each of the two couplers is connected via another coupler to the machine rack so that four couplers form a W and/or M in a projection. The drives are designed as feedforward units run on slewable bearings at the machine rack, these feedforward units being run on slewable bearings at the tool carrier. By adjustment of one feedforward unit or both units the tool carrier can be adjusted within a work area lying in the X-Y plane. A work space is created by adjustment of the skid arranged on the tool carrier in Z-direction. This machine tool is built of a relatively complicated structure. And it also takes relatively much space. Another disadvantage is seen in the way of how the couplers are arranged, meaning that they are constantly subjected to torsional stresses in case of loads attacking at the cantilevered Z-skid and acting in the X-Y-plane. It represents a very unfavorable load case for the couplers which can be counteracted only by increasing the torsional stiffness.